Question

Choose the items that complete the sentence about the key features of f(x) = 8x. The y-intercept is Choose... , the asymptote is y = Choose... , and the range is y > Choose... .

Answer 1

Answer:

I suppose that the equation is:

f(x) = 8/x

(You wrote 8x, this is a linear function, so it has no asymptotes, then I assume that the actual function was 8/x)

The y-intercept is the value such that  f(x) = 0

Notice that there is no value of x such that 8/x = 0  (if the numerator is never zero, then the quotient can't be zero)

So we do not have an y-intercept.

The asymptote:

Here we have four:

if x tends to zero from the negative side, then:

8/x tends to negative infinity.

if x tends to zero from the positive side, then:

8/x tends to positive infinity.

These two asymptotes can be written as:

$\lim_{n \to \_-0} \frac{8}{x} = -\infty\\ \lim_{n \to \_+0} \frac{8}{x} = +\infty$

We also have two when x tends to plus infinity (and 8/x goes to zero) and when x tends to negative infinity, such that the function tends to zero again, these two can be written as:

$\lim_{n \to \infty} \frac{8}{x} = 0\\ \lim_{n \to -\infty} \frac{8}{x} = 0$

Finally, the range:

The only value that y never reaches (only on limits) is:

y = 0

Then the range is the set of all real numbers except the zero, or:

R :  { x ∈ R / {0} }